For me, it's primarily a consumer safety and freedom of choice issue. In short, I don't trust the EFTPOS system to cover me properly when things hit the fan, based on past experience and first hand knowledge.
I've spent a good portion of my working life dealing with chargeback resolutions for various companies. The sheer volume of paperwork, documentation and investigation required for dealing with these is an unmitigated nightmare. I once had to spend half a day in a basement storage room searching for a single piece of paper to resolve a $1.5k chargeback claim. It wasn't fun.
Fraud recovery through the EFTPOS system, and particularly chargebacks handling (duplicate processing due to system error, etc) is much more difficult to deal with. Also most of the fraud detection platforms operated by the 'four pillocks' (my banking friend's nickname for the four pillars) are as yet not extended far enough into the EFTPOS transaction framework.
I know that there's concrete systems in place to detect Visa/MC fraud, the response is instantaneous, and the additional fraud protection coverage provided by my debit card will protect me as soon as things do go south.
And let's be honest, Woolworths are just being grubby here. They've done this solely to further pad their bottom line with the hundreds of thousands of dollars they earn from merchant acquiring from EFTPOS.
I know how much companies pay in transaction fees, and massive networks like Woolworths with their astronomical transaction volumes are generally paying cents per transaction for Visa/MC debit.
The cost of accepting Visa/MC debit is offset completely by the reduction in business costs achieved through reduced costs of cash management (staff time, reconciliation, transport, security).
Its a penny wise, pound foolish strategy they've taken here and I have already voted with my wallet.